Single Imputation Methods and Confidence Intervals for the Gini Index

This research has been partially supported by the Ministry of Economy, Industry and Competitiveness, the Spanish State Research Agency (SRA) and European Regional Development Fund (ERDF) (project reference ECO2017-86822-R). This research has been partially supported by the Ministry of Economy, Industry and Competitiveness, the Spanish State Research Agency (SRA) and European Regional Development Fund (ERDF) (project reference ECO2017-84138-P).The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods when they are applied to the estimation of the Gini index, a popular measure of inequality used in many studies. Various methods for constructing confidence intervals for the Gini index are also empirically evaluated. We consider several empirical measures to analyse the performance of estimators and confidence intervals, allowing us to quantify the magnitude of the non-response bias problem. We find extremely large biases under certain non-response mechanisms, and this problem gets noticeably worse as the proportion of missing data increases. For a large correlation coefficient between the target and auxiliary variables, the regression imputation method may notably mitigate this bias problem, yielding appropriate mean square errors. We also find that confidence intervals have poor coverage rates when the probability of data being missing is not uniform, and that the regression imputation method substantially improves the handling of this problem as the correlation coefficient increases.Ministry of Economy, Industry and Competitiveness Spanish State Research Agency (SRA)European Commission ECO2017-84138-

The level matrix of a tree and its spectrum

Given a rooted tree $T$ with vertices $u_1,u_2,\ldots,u_n$, the level matrix $L(T)$ of $T$ is the $n \times n$ matrix for which the $(i,j)$-th entry is the absolute difference of the distances from the root to $v_i$ and $v_j$. This matrix was implicitly introduced by Balaji and Mahmoud~[{\em J. Appl. Prob.} 54 (2017) 701--709] as a way to capture the overall balance of a random class of rooted trees. In this paper, we present various bounds on the eigenvalues of $L(T)$ in terms of other tree parameters, and also determine the extremal structures among trees with a given order. Moreover, we establish bounds on the mutliplicity of any eigenvalue in the level spectrum and show that the bounds are best possible. Furthermore, we provide evidence that the level spectrum can characterise some trees. In particular, we provide an affirmative answer to a very recent conjecture on the level energy (sum of absolute values of eigenvalues).Comment: 17 pages, 01 figur

An Intelligent Approach to Reducing Plant Disease and Enhancing Productivity Using Machine Learning

Plant diseases are a normal part of the natural world, and they are one of the many ecological processes that work together to keep the vast number of living organisms in the world in a state of equilibrium with one another. Each plant cell has its own set of signalling pathways that help the plant fight off viruses, animals, and insects. Concerns have been raised about whether or not it is possible to use machine learning to make crop predictions based mostly on weather data. The goal of the research is to help users choose the right crop to grow so that they can maximise their yield and, as a result, the money they make from the project. In a rural area where almost half the people work in agriculture, one of the most important problems is when farmers can't use traditional or other non-scientific methods to choose a crop that will grow well in their soil. Researchers can't make use of case studies as well as they could because there isn't enough correct and up-to-date information available. With the resources at our disposal, we have proposed a model that makes use of random forests and the genetic algorithm. This model has the potential to solve this problem by providing predictive insights on the long-term viability of crops and recommendations based on machine-reading models that have been trained to take important environmental parameters into consideration.

Quantifying the Predictability of Evolution at the Genomic Level in Lycaeides Butterflies

Stephen Jay Gould, a great scientist and evolutionary biologists, suggested that if we could replay the tape of life, we would not have observed similar course of events because evolution is stochastic and if affected by several events. Since then, the possibility that evolution is repeatable or predictable has been debated. Studies using large-scale evolution experiments, long-term data for individual populations, and controlled experiments in nature, have demonstrated phenotypic and genetic convergence in several taxa. These studies suggest that despite some randomness, predictable evolutionary patterns can emerge on a large temporal and spatial scale. However, a few cases also exist where evolution is unpredictable and stochastic. One way to understand evolutionary predictability better can be to have quantitative estimates of predictability at different heirarchical levels (mutations, genetic, phenotypic). This can help better understand if evolution is predictable and the extent to which it is predictable. My dissertation uses Lycaeides butterflies to identify and quantify evolutionary predictability in different contexts such as on a geographic scale, temporal scale and genomic scale. I accomplished this by sequencing and annotating the genomes of these butterflies across a vast geographic range and on a temporal scale and by comparing natural and experimental populations. My results show that different mechanisms can assist evolution of organisms to adapt to novel environmental challenges, and that the evolutionary changes can be somewhat predictable. Through this work I demonstrate three main findings: first, quantitative estimates of evolutionary predictability indicate that degree of predictability is variable and is highly context-dependent. Second, we can predict evolutionary patterns on a spatial as well as temporal scale, and can predict patterns in nature by controlled laboratory experiments. Additionally, genomic changes underlying repeatability vary across the genome. Lastly, the approach of quantifying predictability can help us better understand the mechanisms which drive evolution and how organisms will evolve in response to similar environmental pressures. These results suggest that evolution can be constrained and if we actually replay the tape of life, we could see a considerably similar outcome in biodiversity compared to what Gould predicted

Measuring the Economic Benefits of Forests in Relation to Households’ Welfare and Forest Dependence in South-western Nigeria

The study assesses the contributions of forest resources income on poverty among rural households in South-western Nigeria. A multi-stage random sampling approach was adopted while descriptive analysis and [Foster-Greer-Thorbecke (FGT 1984) poverty index] were used. Poverty index results showed that 68 percent of the rural households were living below the poverty line in the region. Disaggregated to state level, the highest proportion was found in Osun state (77 percent ), followed by Ogun state (70 percent ) and Oyo state with about 50 percent. The minimum cost required to bring those poor households to the poverty line (that is, to eliminate poverty) across states include: N4, 553, N9, 664 and N8918 in Oyo, Osun and Ogun states respectively. This indicates that poverty is more severe in Osun state followed by Oyo state but less severe in Ogun state. Also, forest income has tendency to stem the tide of poverty in the region. Therefore, Government and authority concerned should increase opportunities for entrepreneurship and employment in forestry while avoiding deforestation and forest degradation